Related papers: Memory Elements: A Paradigm Shift in Lagrangian Mo…
Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the…
Orbital degrees of freedom offer a largely untapped route to emergent dynamical phenomena in correlated quantum materials. However, it remains unclear whether collective orbital states can intrinsically generate both reactive and memory…
A new Lagrangian formulation with complex currents is developed and yields a direct and simple method for modeling three-phase permanent-magnet and induction machines. The Lagrangian is the sum a mechanical one and of a magnetic one. This…
In the standard Lagrangian and Hamiltonian approach to Maxwell's theory the potentials $A^{\mu}$ are taken as the dynamical variables. In this paper I take the electric field $\vec{E}$ and the magnetic field $\vec{B}$ as the the dynamical…
The conventional Landau-Lifshitz-Gilbert (LLG) equation is a widely used tool to describe dynamics of local magnetic moments, viewed as classical vectors of fixed length, with their change assumed to take place simultaneously with the…
In the present article, we discuss a modification of classical electrodynamics in which ``ordinary'' point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the…
A memristor is an electrical element, which has been conjectured in 1971 to complete the lumped circuit theory. Currently, researchers use memristors emulators through diodes and other passive (or active) elements to study circuits with…
We extend an axiomatic approach to classical electrodynamics, which we developed recently, to the case of non-vanishing magnetic charge. Then two axioms, namely those of the existence of the Lorentz force (Axiom 2) and of magnetic flux…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
We give a Lagrangian description of an electric charge in a field sourced by a continuous magnetic monopole distribution. The description is made possible thanks to a doubling of the configuration space. The Legendre transform of the…
It is well known that a covariant Lagrangian for relativistic charged particles can lead to a vanishing Hamiltonian. Alternatively, it is shown that using a "space+time" Lagrangian leads to a new canonical momentum and minimal coupling rule…
Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that…
The invariance of the Lagrangian under time translations and rotations in Kepler's problem yields the conservation laws related to the energy and angular momentum. Noether's theorem reveals that these same symmetries furnish generalized…
In (3+1) Hamiltonian form, the conditions for the electric/magnetic invariance of generic self-interacting gauge vector actions and the definition of the duality generator are obvious. Instead, (3+1) actions are not intrinsically Lorentz…
It is observed that the inductive and capacitive features of the memristor reflect (and are a quintessence of) such features of any resistor. The very presence of the voltage and current state variables, associated by their electrodynamics…
An operational (measurement based) scheme that connects measurement invasiveness and the presence of non-classical memory effects in open quantum systems is defined. Its underlying theoretical basis relies on a non-invasive measurability of…
Memristive systems are generalisations of memristors, which are resistors with memory. In this paper, we present a quantum description of memristive systems. Using this model we propose and experimentally demonstrate a simple and practical…
In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed unity, and the unitarity principle as the requirement that…
Memristors are nonlinear two-terminal circuit elements whose resistance at a given time depends on past electrical stimuli. Recently, networks of memristors have received attention in neuromorphic computing since they can be used as a tool…
Most capacitors do not satisfy the conventional assumption of a constant capacitance. They exhibit memory which is often described by a time-varying capacitance. It is shown that the classical relation, $Q\left(t\right)=CV\left(t\right)$,…